Number worksheet — GCSE Higher

1.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

2.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

3.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

4.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

5.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

6.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

7.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

8.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

10.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

11.A country has an area of 25,000,000 hectares. Write this area in standard form.

12.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

13.Work out −(−3)⁴ + (−3)³

14.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

15.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09